As greater and greater amounts of data are produced that provide indications of some measurable quantity, the processing of these vast amounts of data becomes more difficult to arrive at meaningful results. Higher frequency systems such as microwave and the like, and the optical portion of the electromagnetic spectrum can and do produce choking amounts of data for processors which were otherwise felt to be quite adequate. Matrix-matrix multiplying using an all electronic systolic array architecture was advocated by H. T. Kung, see Introduction to VLSI Systems, Addison-Wesley, 1980, pp. 271-292 by C. Mead and L. Conway. The electronic systolic array was limited to a two-dimensional architecture and employed silicon technology along with an all electronic implementation. Operation in the two-dimensional mode was felt to be a limitation on the mathematical operation of matrix-matrix multiplication and led to the incorporation of optical techniques.
An extensive mathematical study has been made regarding the use of optical correlation techniques involving coherent light for performing matrix-matrix and matrix-vector multiplication by R. A. Heinz, J. O. Artman, and S. H. Lee, in their article entitled "Matrix Multiplication by Optical Methods," Applied Optics, vol. 9, pp. 2161-2168, September 1970. The optical correlation techniques of Heinz, Artman and Lee were experimentally demonstrated for matrices of the order of 2 by D. P. Jablonowski, R. A. Heinz, and J. O. Artman, as reported in their article entitled "Matrix Multiplication by Optical Methods: Experimental Verification," Applied Optics, vol. 11, pp. 174-178, January 1972. The technique developed and verified was found to have one limiting feature in that as the matrix order increases, the number of unwanted circular distributions of light appearing in the output plane of the processor rapidly escalates thus reducing the light available at those positions corresponding to product matrix element information. As follow-ons to this technique, there have been a number of other approaches investigated using incoherent light for performing matrix-vector multiplication. One which comes to mind is the preliminary study in this area which describe the computation of one-dimensional discrete Fourier transforms as discussed by Richard P. Bocker in his article entitled "Matrix Multiplication Using Incoherent Optical Techniques," Applied Optics, vol. 13, pp. 1670-1676, July 1974. Since, cosine and Walsh-Hadamard transforms, as well as a variety of linear filtering operations were discussed by Richard P. Bocker in his Ph.D. dissertation, "Optical Matrix-Vector Multiplication and Two-Channel Processing with Photodichroic Crystals," which is available at the University of Arizona, Tuscon, 1975 (Univ. Microfilms 75-26 925).
The technical feasibility of Bocker's particular approaches were demonstrated for matrices of order 32 using an optical device earlier developed by Keith Bromley and is fully explained in his article "An Optical Incoherent Correlator, " Optica Acta, vol. 21, pp. 35-41, January 1974. Mr. Bromley made the demonstrations for performing correlation and convolution operations with incoherent light. In the original version of an optical correlator, a single light emitting diode, photographic film transparency, mechanical scanning mirror, and a vidicon detector were employed. More recently, Michael A. Monohan, Richard P. Bocker, Keith Bromley and Anthony Louie discovered that the scanning mirror and vidicon detector could be replaced by a solid-state area-array coupled device thus greatly reducing the size of the processor, see their article entitled "Incoherent Electrooptical Processing with CCD's," International Optical Computing Conference Digest (IEEE Catalog 75 CH0941-5C), April 1975 and an article by Monahan, Bromley and Bocker entitled "Incoherent Optical Correlators", Proceedings of the IEEE, vol. 65, pp. 121-129, January 1977. It was found that matrix-vector multiplying operations involving matrices of order 128 can be and are presently performed using this approach.
A second technique for computing matrix-vector products using incoherent light involves the use of a linear array of light emitting diodes, an optical transparency, and a linear array of photodetectors. The groundwork and development for this technique were made by J. W. Goodman, A. R. Dias, and L. M. Woody, in their article entitled "Fully Parallel, High-Speed Incoherent Optical Method for Performing Discrete Fourier Transforms," in Optics Letters, vol. 2, pp. 1-3, January 1978. The architecture of the publication has the advantage that the data vector information may be entered in parallel, thus allowing for higher throughput rates. The feasibility of this approach has been demonstrated for matrices of order 10. Combining this architecture with a one-dimensional adder in a feedback loop gives rise to an iterative electrooptical processor, see the article by D. Psaltis, D. Casasent, M. Carlotto, entitled "Iterative Color-Multiplexed, Electro-Optical Processor," Optics Letters, vol. 4, pp. 348-350, November 1979. With this capability it is possible to perform other higher-level matrix operations such as the solution of simultaneous algebraic equations, least squares approximate solution of linear systems, matrix inversions, and eigensystem determinations just to mention a few. These solutions have, in fact, been demonstrated by B. V. K. Vijaya Kumar and D. Casasent, in "Eigenvector Determination by Iterative Optical Methods," Applied Optics, vol. 20, pp. 3707-3710, November 1981 and by M. Carlotto and D. Casasent in "Microprocessor-Based Fiber-Optic Iterative Optical Processor," Applied Optics, vol. 21, pp. 147-152, January 1982.
Even more recently, much attention has been focused on implementing parallel processing architectures for performing a variety of matrix operations using exclusively electronic components. In addition to the work by H. T. Kung, identified above he has shown further efforts in this field in his two articles entitled "Special-Purpose Devices for Signal and Image Processing: An Opportunity in Very Large Scale Integration (VLSI)," SPIE, vol. 241, pp. 76-84, 1980 and "Why Systolic Architectures?," Computer, vol. 15, pp. 37-46, January 1982. Combining VLSI/VHSIC technology with systolic array processing techniques should give rise to increased signal-processing capabilities by at least a factor of 100, see J. J. Symanski's article entitled "A Systolic Array Processor Implementation," SPIE, vol. 298, 1981. Already a two-dimensional systolic array test bed has been designed and fabricated for validating many of the proposed architectures and algorithms envisioned, note J. J. Symanski's article "Progress on a Systolic Processor Implementation," SPIE, vol. 341, 1982. In addition a similar all electronics parallel approach has been proposed by J. M. Speiser and H. J. Whitehouse in their presentation entitled "Parallel Processing Algorithms and Architectures for Real-Time Signal Processing," SPIE, vol. 298, 1981 using an engagement array architecture.
As it turns out, the proposed new systolic/engagement type of architectures are not restricted to solely all electronic implementations. For example, an acoustooptical approach using incoherent light for performing matrix-vector multiplication employing the systolic/engagement array architecture recently has been described by H. J. Caulfield and W. T. Rhodes in their presentation entitled "Acousto-Optic Matrix-Vector Multiplication," that was presented at the Annual Meeting of the Optical Society of America, Kissimmee, FL, October 1981. Their acoustic optic processor uses a linear array of light emitting diodes for inputting the matrix information, and acousto-optic travelling wave modulator for inputting the vector information, and a linear array charge-coupled device for computing the desired output vector information. Their approach had the advantage that the input vector and matrix information may be entered in real-time.
Thus there is a continuing need in the state-of-the-art for a device for performing the mathematical operation of matrix-matrix multiplication using electrooptical technology to have the capability for handling increased amounts of data in real time.